Stacking-sequence optimization for buckling of laminated plates by integer programming

Initial sizing optimisation of anisotropic composite panels with T-shaped stiffeners

“…The value of Y k is 1, when more than 4 plies of the same orientation are stacked together [13], otherwise it is 0.…”

“…Fukunaga and Vanderplaats [12] used lamination parameters and mathematical programming (MP) techniques to carry out stiffness optimisation of cylindrical shells with orthotropic properties. Haftka and Walsh [13] used integer-programming techniques to carry out lay-up optimisation under buckling constraints on symmetric and balanced laminated plates. They used zero-one integers as design variables that were related to stiffness properties via lamination parameters and showed that the problem was linear.…”

Optimization of composite plates subjected to buckling and small mass impact using lamination parameters

“…Both authors have demonstrated that the optimum project varies in accordance to the plate aspect ratio and the load ratio (N y /N x ). On the other hand, Haftka and Walsh [9] proposed an optimization procedure based on the lamination parameters but limited to lamination angles: 0 o , 45 o , -45 o and 90 o . The ply orientations chosen are justified by the good practices of composite laminate manufacturing.…”

“…Therefore, the structural design optimization to withstand the buckling phenomenon has been constantly addressed in the last years (e.g., Refs. [5][6][7][8][9][10][11]. However, studies on the effects of impact damage on the buckling load of aeronautical structures are scarce in the literature.…”

Optimum design for buckling of arbitrary shaped ribs under uncertain loadings

“…In most investigations conducted in the past addressing buckling optimisation of plates (1)(2)(3)(4)(5) , the distribution of the applied loading remains fixed and uniform during the optimisation procedure such that the load magnitude is the parameter to be maximised (6) . For instance, when plates subjected to biaxial loads are studied, a constant load ratio is considered as a relation between the normal loads along each axis whose distributions are uniform.…”